This depends on whether you are married or not. This also assumes the father is a cooperative party.
If you are not married, the father can be placed on the birth certificate if he acknowledges paternity o the child or through a court order. If the father is unavailable at the time of birth, his name may be added later.
If you are married there is already a presumption in Florida that your husband is the father of the child (yes even if you got pregnant by another man.) Paternal acknowledgment is automatic, and the father may be listed without being present.
As far as the naming convention goes, you may give your child any name you choose without listing the father. If you list the child with your last name, you may change that name anytime before the child's first birthday.
If you need the father to acknowledge paternity, I believe there is a form available from the Bureau of Vital Statistics. Alternatively you could have the father sign an affidavit acknowledging paternity as well.
Best of luck to the child, you, and the father.
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